A successive approximation register (SAR) analog-to-digital converter (ADC) converts analog signals into digital signals using a binary search method. SAR ADCs exhibit high conversion efficiency with moderate resolution and bandwidth, and attempt to reduce ADC noise. Noise-shaping can be used to decrease noise and improve resolution of SAR ADCs. However, attempts at noise-shaping have only been able to achieve first-order noise shaping. Additionally, noise-shaping methods use active operational transconductance amplifiers which consume extra power, and take extra area on the chip.